Class Title1: Math Grade Level: 4 th Grade Nine Weeks: 1 st Nine Weeks Unit 1 CCSS: Multiplication and Division Concepts Students will be able to Translate comparative situations into drawings and equations with a symbol for the unknown and unknowns in all 3 locations. (4.OA.2) Solve word problems involving multiplicative comparison using drawings and (multiplication or division) equations with a symbol for the unknown number and unknowns in all 3 locations. (4.OA.2) Explain the difference between additive comparison and multiplicative comparison using visuals and words. (4.OA.2) Read and write whole numbers up to a million using standard, word, and expanded form. (4.NBT.2) Compare two multi-digit (up to a million) numbers. (4.NBT.2) Use manipulatives, pictures, and language to show the relationship between the numerals and their place value representations in multiple ways. (4.NBT.2) Identify all factor pairs for any given number 1-100. Recognize that a whole number is a multiple of each of its factors. (4.OA.4) Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. (4.OA.4) o o o o o Use the four operations with whole numbers to solve problems. Generalize place value understanding for multi-digit whole numbers. Gain familiarity with factors and multiples. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use the four operations with whole numbers to solve problems.
Determine whether a given whole number in the range 1-100 is prime or composite. (4.OA.4) Use visuals, symbols and/or language to explain their reasoning. (4.OA.4) Multiply up to 4-digit by 1-digit numbers and 2-digit by 2-digit numbers. (4.NBT.5) Use place value manipulatives to represent multiplication calculations. Illustrate and explain the calculation by using written equations, rectangular arrays, and area models. (4.NBT.5) Find whole-number quotients and remainders with up to fourdigit dividends and one-digit divisors. Illustrate and explain the calculation by using written equations, rectangular arrays, and area models. (4.NBT.6) Use place value manipulatives to represent division calculations. (4.NBT.6) Use the relationship between multiplication and division to explain calculations. (4.NBT.6) Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations and represent those problems using equations with a variable standing for the unknown quantity. Interpret remainders when solving multi-step word problems (4.OA.3) Assess the reasonableness of answers using mental computation and estimation strategies, including rounding. (4.OA.3)
Class Title: 4th Grade Math Grade Level: Math Nine Weeks: 2 nd Nine Weeks Unit 2 CCSS: Fractions: Equivalence and Operations Recognize and generate equivalent fractions. (4.NF.1) Compare two fractions with different denominators and different numerators by representing the fractions with symbols, visual models and words, and by comparing to a benchmark fraction using symbols, visual models, and words. (4.NF.2) Identify if comparisons are valid or invalid and explain why. (4.NF.2) Represent unit fractions as a fraction with a numerator of 1 with manipulatives, pictures, symbols, language, and real-life examples. (4.NF.3) Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. (4.NF.3) Add and Subtract mixed numbers with like denominators and model the decomposition of the mixed numbers into unit fractions using manipulatives, pictures, symbols, language, and real-life examples. (4.NF.3) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators using visual models and/or equations. (4.NF.3) o o o o Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit. Represent and interpret data.
Represent multiplication of a fraction by a whole number as repeated addition using area or linear models. (4.NF.4) Represent that a fraction, such as ¾, is made up of 3 unit fractions of ¼ using a multiplication equation, such as 3 x ¼ = ¾. (4.NF.4) Multiply a fraction by a whole number by decomposing the fraction into a multiple of a unit fraction such as ¾ x 2 = 3 x 2 x ¼ which equals 6/4, using manipulatives, pictures, symbols, language, and real-life examples. (4.NF.4) Represent improper fractions with visual models to demonstrate their relationship to the two closest whole numbers. (4.NF.4) Solve word problems involving multiplication of any fraction by a whole number by using visual models and/or equations. (4.NF.4) Identify relative sizes of measurement units within one system (customary) of units including lb. and oz; hr, min, and sec. (4.MD.1) Represent the larger unit of measure in terms of the smaller unit of measure within the same measurement system (customary), including lb and oz; hr, min, and sec, using manipulatives, pictures, language and/or equations. (4.MD.1) Record customary measurement equivalents in a two column table. (4.MD.1) Use pictures and equations to represent and solve addition, subtraction, multiplication, and division word problems involving distance, elapsed time, liquid volumes, and masses of objects (customary system). (4.MD.2)
Measure objects to the nearest ½, ¼ or 1/8 of a unit. (4.MD.4) Make a line plot to display a set of measurements to the nearest ½, ¼, or 1/8 of a unit. (4.MD.4) Solve problems involving addition and subtraction of fractions by using information presented in line plots, (i.e. range). (4.MD.4) Nine Weeks: 3rd Nine Weeks Unit 3 CCSS: Decimals Represent a fraction with denominator 10 as an equivalent fraction with denominator 100. (4.NF.5) Add two fractions with denominators 10 and 100 using manipulatives, pictures, written symbols, and language to explain the process. (4.NF.5) Write fractions with 10 and 100 in the denominator as decimals. (4.NF.6) Compare two decimals to the hundredths using <, >, =. (4.NF.7) Identify if decimal comparisons are valid or invalid and explain why. (4.NF.7) Justify the conclusions using manipulatives, pictures and/or language. (4.NF.7) o Understand decimal notation for fractions, and compare decimal fractions.
Nine Weeks: 3rd Nine Weeks Unit 4 CCSS: Computation Applications Generate a pattern that follows a rule. (4.OA.5) Given a pattern, identify the rule and extend the pattern and also identify apparent features of a pattern that follows a given rule, which are not explicit in the rule itself. (4.OA.5) Round multi-digit whole numbers to a given place. (4.NBT.3) Explain the rounding process using visuals and/or language. (4.NBT.3) Add and subtract multi-digit whole numbers up to 1,000,000. (4.NBT.4) Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations. (4.OA.3) Represent multi-step word problems using equations with a variable standing for the unknown quantity. (4.OA.3) Assess the reasonableness of answers using mental computation and estimation strategies, including rounding. (4.OA.3) Represent the larger unit of measure in terms of the smaller unit of measure within the metric system, using manipulatives, pictures, language and/or equations. (4.MD.1) Record measurement equivalents in a two-column table. o o o o o Generate and analyze patterns. Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use the four operations with whole numbers to solve problems. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
(4.MD.1) Use pictures and equations to represent and solve addition, subtraction, multiplication and division word problems involving measurement, distance, liquid volumes and masses of objects.(4.md.2) Solve problems involving area and perimeter of rectangles using visuals and equations that represent the formulas for area and perimeter of rectangles. (4.MD.3) Nine Weeks: 4 th Nine Weeks Unit 3 CCSS:Geometry Draw points, lines, line segments, rays, right angles, acute angles, obtuse angles, perpendicular lines, and parallel lines. (4.G.1) Classify 2-dimensional figures based on the presence or absence of parallel or perpendicular lines and right, acute or obtuse angles. (4.G.2) Identify and classify triangles. Label the categories of triangles (right triangles, scalene, isosceles) (4.G.2) Recognize a line of symmetry for a two-dimensional figure as a fold-line, where the figure can be folded into matching parts. (4.G.3) Determine whether a figure has one or more lines of symmetry o o Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Geometric measurement: understand concepts of angle and measure angles.
and draw lines of symmetry. (4.G.3) Identify the components of an angle and the number of degrees in a circle. (4.MD.5) Use visuals and language to show the relationship between the components of an angle to a circle. (i.e. the center of the circle is the endpoint of the rays of the angle) (4.MD.5) Measure angles in whole-number degrees using a protractor. (4.MD.6) Sketch angles of a specified measure. (4.MD.6) Use diagrams, manipulatives and equations to show that angle measure is additive. (4.MD.7) Solve addition and subtraction problems to find unknown angles on a diagram of adjacent angles. (non-overlapping angles) (4.MD.7)
Class Title:Math Grade Level:5 th Grade Nine Weeks:1 nine weeks Unit: Whole Number Computation and Application Fluently multiply multi-digit whole numbers. (5.NBT.5) Divide up to 4-digit whole numbers by up to 2-digit whole numbers by using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (5.NBT.6) Use parentheses, brackets, and braces in numerical expressions. And evaluate those expressions.(5.oa.1) Perform operations with multi-digit whole numbers and with decimals to hundredths. Write and interpret numerical expressions. Nine Weeks 1st nine weeks Unit: Unit 2 Volume Students will be able to Define volume as the measurement of the space inside a solid three-dimensional figure. (5.MD.3) Identify and describe unit cubes as representing 1 cubic unit of volume, and how they are used to measure volume of threedimensional shapes. (5.MD.3) Model how a solid figure is packed with unit without gaps or overlaps to measure volume. (5.MD.3) Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Understand the place value system.
Use the term cubic units to describe units of volume measurement. (5.MD.3) Measure volumes by counting cubes first with manipulatives and then by pictures using cubic cm., cubic in., cubic ft., and improvised units. (5.MD.4) Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes. (5.MD.5) Prerequisite: Find the volume of a right rectangular prism by finding the area of the base and using repetitive addition to add the layers of height. Find the volume of a right rectangular prism by finding the area of the base and multiplying by the number of layers in the prism (height). (5.MD.5) Show that the volume is the same as it would be if volume were found by multiplying the edge lengths. (5.MD.5) Build a right rectangular prism model to represent a 3 factor multiplication expression. (5.MD.5) Apply the formula to find volumes of right rectangular prisms with whole number edge lengths in real world and mathematical problems. (5.MD.5) Find the volume of composite rectangular prisms by adding the volumes of the non-overlapping parts and applying the technique to solve real world problems. (5.MD.5)
Nine Weeks: 2 nd nine weeks Unit: Unit 3 Fractions Computation and Application Students will be able to Use equivalent fractions as a strategy to add and subtract fractions. Add fractions with unlike denominators) by replacing given Apply and extend previous understandings of multiplication and division to fractions with equivalent fractions. (5.NF.1) multiply and divide fractions. Add mixed numbers with unlike denominators) by replacing given Convert the measurement units within a given measurement system. fractions with equivalent fractions. (5.NF.1) Subtract fractions with unlike denominators by replacing given fractions with equivalent fractions. (5.NF.1) Represent and interpret data. Subtract mixed numbers with unlike denominators by replacing given fractions with equivalent fractions (5.NF.1) Solve word problems involving addition of fractions referring to the same whole, including cases of unlike denominators using visual fraction models and/or equations. (5.NF.2) Solve word problems involving subtraction of fractions referring to the same whole, including cases of unlike denominators using visual fraction models and/or equations. (5.NF.2) Use benchmark fractions and number sense to estimate mentally and assess reasonableness of answers. (5.NF.2) Interpret a fraction as division of the numerator by the denominator. (5.NF.3) Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers using visual fraction models or equations. (5.NF.3) Multiply a fraction by a whole number. (5.NF.4) Use visual fraction models and/or language to interpret multiplication of a fraction by a whole number as multiplying the numerator by the whole and dividing by the denominator. (5.NF.4) Multiply a fraction by a fraction. (5.NF.4) Use visual fraction models and/or language to interpret
multiplication of fractions as multiplying numerators and multiplying denominators. (5.NF.4) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. (5.NF.4) Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. (5.NF.4) Use language and visuals to explain how multiplication of fractions represents scaling (resizing). (5.NF.5) Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication using visuals, real-life situations and/or language. (5.NF.5) Explain why multiplying a number by a fraction less than 1, results in a smaller product using visuals, equations, language and real-life examples (5.NF.5) Explain why multiplying a number by a fraction equal to 1, results in the same product using visuals, equations, language and real-life examples (5.NF.5) Explain why multiplying a number by a fraction greater than 1, results in a larger product using visuals, equations, language and real-life examples (5.NF.5) Solve real world problems involving multiplication of fractions using visual fraction models and equations. (5.NF.6) Solve real world problems involving multiplication of mixed numbers using visual fraction models and equations. (5.NF.6) Divide a unit fraction by a non-zero whole number using manipulatives, pictures, equations, real life examples and language. (5.NF.7) Divide a non-zero whole number by a unit fraction using manipulatives, pictures, equations, real life examples and language. (5.NF.7) Solve real world problems involving division of a unit fraction by a
non-zero whole number and division of a non-zero whole number by a unit fraction using visual models and equations to represent the problem. (5.NF.7) Convert measurements within the metric system to solve multi - step, real world problems. (100cm = 1 meter) (5.MD.1) Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8) (5.MD.2) Use addition, subtraction, multiplication, and division of fractions to solve problems involving information presented in line plots. (5.MD.2) Nine Weeks: 3rd nine weeks Unit: Unit 4 Decimal Computation and Applications Model and explain that the value of a digit changes as you move to the left (10 times more) or to the right (1/10 less) using manipulatives, pictures, and/or language. (5.NBT.1) Represent and model the pattern of zeros that occurs when multiplying by powers of 10. (103 = 10x10x10=1000) (5.NBT.2) Represent and explain the patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. (5.NBT.2) Understand the place value system Convert the measurement within a given measurement system.
Represent and model the use of a whole number exponent to denote powers of 10. (5NBT.2) Read decimals to thousandths using number names. (5.NBT.3) Write decimals to thousandths using base-ten numerals and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 (1/10) + 9 x (1/100) + 2 x (1/1000).(5.NBT.3) Compare two decimals to thousandths based on meaning of the digits in each place, using >, =, and < symbols to record the results of comparisons. (5.NBT.3) Round decimals to any place. (5.NBT.4) Convert measurements within the metric system to solve multistep, real world problems. (100cm = 1 meter) (5.MD.1) Use concrete models, pictorial representations, written symbols, and language to show addition, subtraction, multiplication, and division of decimals to hundredths.(5.nbt.7)
Nine Weeks: 4th nine weeks Unit: Unit 5 2 Dimensional Geometry Identify two-dimensional shapes that can be classified into more than one category based on their attributes. (5.G.3) Explain why figures belong in a category or multiple categories. (5.G.3) Classify two-dimensional figures in a hierarchy based on properties (5.G.4) Classify two-dimensional figures into categories based on their properties. Nine Weeks: 4 th nine weeks Unit: Unit 6 Coordinate Geometry Generate two numerical patterns using two given rules. (5.OA.3) Identify numerical relationships between corresponding terms in 2 different expressions. (5.OA.3) Form ordered pairs from the two patterns. (5.OA.3) Graph the ordered pairs on the coordinate plane. (5.OA.3) Graph on the coordinate plane. (5.G.1) Identify, describe and explain the relationship between the names of the components of the coordinate plane including origin, x- and Analyze patterns and relationships Graph points the coordinate plane to solve real-world and mathematical problems. Write and interpret numerical expressions.
y- axis and x- and y- coordinates. (5.G.1) Explain how to plot points on the coordinate plane. (5.G.1) Graph points from a real -life situation, oral/written language or a written expression on the coordinate plane. (5.G.2) Explain the relationship or value of the plotted points in the context of the situation. (5.G.2) Nine Weeks: t nine weeks Unit: Nine Weeks: t nine weeks Unit:
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 1st Nine Weeks Unit 1 CCSS: Fractions and Decimals Students will be able to Compute quotients of fractions divided by fractions. (6.NS.1) Explain the meaning of a quotient determined by division of fractions, using visual fraction models, equations, real-life situations, and language. (6.NS.1) Divide multi-digit numbers fluently using the standard algorithm. (6.NS.2) Apply and extend previous understandings of multiplication and division to divide fractions by fractions Compare fluently with multi-digit numbers and find common factors and multiples Solve real-world and mathematical problems involving area, surface area, and volume Fluently add, subtract, multiply and divide decimals to solve problems. (6.NS.3)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 1st Nine Weeks Unit 2 CCSS: Ratios, Rates, and Proportions Students will be able to Use ratio language to describe a ratio relationship between two quantities. (6.RP.1) Represent a ratio relationship between two quantities using manipulatives and/or pictures, symbols and real-life situations. (a to b, a:b, or a/b) (6.RP.1) Understand ratio concepts and use ratio reasoning to solve problems. Represent and analyze quantitative relationships between dependent and independent variables. Represent unit rate associated with ratios using visuals, charts, symbols, real-life situations and rate language. (6.RP.2) Use ratio and rate reasoning to solve real-world and mathematical problems. (6.RP.3) Make and interpret tables of equivalent ratios. (6.RP.3) Plot pairs of values of the quantities being compared on the coordinate plane. (6.RP.3) Use multiple representations such as tape diagrams, double number line diagrams, or equations to solve rate and ratio problems. (6.RP.3) Solve unit rate problems (including unit pricing and constant speed). (6.RP.3)
Solve percent problems, including finding a percent of a quantity as a rate per 100 and finding the whole, given the part and the percent. (6.RP.3) Use variables to represent two quantities in a real-world problem that change in relationship to one another. (6.EE.9) Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. (6.EE.9) Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (6.EE.9)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 2 nd Nine Weeks Unit 3 CCSS: Rational Numbers Skills: Students will be able to Identify an integer and its opposite and the directions they represent in real-world contexts. (6.NS.5) Use integers to represent quantities in real-world situations (above/ below sea level) (6.NS.5) Apply and extend previous understandings of numbers to the system of rational numbers. Solve real-world and mathematical problems involving area, surface area, and volume. Understand the meaning of 0 and where it fits into a situation(6.ns.5) Represent and explain the value of a rational number as a point on a number line (6.NS.6) Recognize that a number line can be both vertical and horizontal (6.NS.6) Represent a number and its opposite equidistant from zero on a number line. (6.NS.6) Identify that the opposite of the opposite of the number is itself. (6.NS.6) Incorporate opposites on the number line or plot opposite points on a coordinate grid where x and y intersect at zero. (6.NS.6)
Represent signs of numbers in ordered pairs as locations in quadrants on the coordinate plane and explain the relationship between the location and the signs. (6.NS.6) Represent and explain reflections of ordered pairs on a coordinate plane (6.NS.6) Locate and position integers and other rational numbers on horizontal or vertical number lines (6.NS.6) Locate and position integers and other rational numbers on a coordinate plane. (6.NS.6) Identify the absolute value of a number as the distance from zero (6.NS.7) Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (6.NS.7) Use inequalities to order integers relative to their position on the number line(6.ns.7) Write statements of order for rational numbers in real-world contexts. (6.NS.7) Interpret statements of order for rational numbers in real-world contexts. (6.NS.7) Explain statements of order for rational numbers in real-world contexts. (6.NS.7) Represent the absolute value of a rational number as the distance from zero and recognize the symbol x. (6.NS.7)
Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (6.NS.7) Distinguish comparisons of absolute value from statements about order. (Compare rational numbers using absolute value in realworld situations. For negative numbers, as the absolute values increases, the value of the number decreases.) (6.NS.7) Solve real-world problems by graphing points in all four quadrants of the coordinate plane (6.NS.8) Use coordinates to find distances between points with the same first coordinate or the same second coordinate. (6.NS.8) Use absolute value to find distances between points with the same first coordinate or the same second coordinate. (6.NS.8) Draw polygons in the coordinate plane given the coordinates for the vertices (6.G.3) Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. (6.G.3) Solve real-world and mathematical problems involving polygons in the coordinate plane. (6.G.3)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 2 nd Nine Weeks Unit 4 CCSS: Expressions Skills: Students will be able to Write numerical expressions that have whole number exponents. (6.EE.1) Evaluate numerical expressions that have whole number exponents and rational bases.(6.ee.1) Apply previous understandings of arithmetic to algebraic expressions Compare fluently with multi-digit numbers and find common factors and multiples. Write algebraic expressions to represent real life and mathematical situations. (6.EE.2) Identify parts of an expression using appropriate terminology. (6.EE.2) Given the value of a variable, students will evaluate the expression. (6.EE.2) Use order of operations to evaluate expressions. (6.EE.2) Apply properties of operations to write equivalent expressions. (6.EE.3) Identify when two expressions are equivalent. (6.EE.4) Prove (using various strategies) that two equations are equivalent no matter what number is substituted. (6.EE.4)
Identify the factors of any whole number less than or equal to 100. (6.NS.4) Determine the Greatest Common Factor of two or more whole numbers less than or equal to 100. (6.NS.4) Identify the multiples of two whole numbers less than or equal to 12 and determine the Least Common Multiple. (6.NS.4) Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. (6.NS.4)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 3 rd Nine Weeks Unit 5 CCSS: Equations and Inequalities Skills: Students will be able to Recognize that solving an equation or inequality is a process of answering a question: which values from a specified set, if any, make the equation or inequality true? (6.EE.5) Reason about and solve one-variable equations and inequalities. Determine whether a given number in a specified set makes an equation or inequality true with substitution. (6.EE.5) Write variable expressions when solving a mathematical problem or real-world problem, recognizing that a variable can represent an unknown number or any number in a specified set (6.EE.6) Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. (6.EE.7) Write an inequality of the form x > c or x < c to represent a constraint or condition in a mathematical problem or a real-world problem. (6.EE.8) Recognize that inequalities of the form x > c or x < c have infinitely many solutions. (6.EE.8) Represent solutions of inequalities on number line diagrams. (6.EE.8)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 3 rd Nine Weeks Unit 6 CCSS: Geometry Skills: Students will be able to Given irregular figures, students will be able to divide the shape into triangles and rectangles (6.G.1) Given a polygon, students will find the area using the decomposing shapes. (6.G.1) Solve real-world and mathematical problems involving area, surface area, and volume. Given a polygon students will calculate the area by decomposing into composite figures (triangles and rectangles). (6.G.1) Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. (6.G.2) Calculate the volume of a right rectangular prism. (6.G.2) Apply the formula to solve real world mathematical problems involving volume with fractional edge lengths. (6.G.2) Represent 3D figures using nets of triangles and rectangles. (6.G.4) Solve real world problems involving surface areas using nets. (6.G.4)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 4 th Nine Weeks Unit 7 CCSS: Statistics Skills: Students will be able to Identify statistical questions. (6.SP.1) Determine if questions anticipate variability in the data related to the question and account for it in the answers. (6.SP.1) Represent a set of data collected to answer a statistical question and describe it by its center, spread, and overall shape. (6.SP.2) Develop understanding of statistical variability Summarize and describe distributions Understand ratio concepts and use ratio reasoning to solve problems Represent and explain the difference between measures of center and measures of variability. (6.SP.3) Display numerical data in plots on a number line. (6.SP.4) Display numerical data in dot plots. (6.SP.4) Display numerical data in histograms. (6.SP.4) Display numerical data in box plots. (6.SP.4) Use language to summarize numerical data sets in relation to their context. (6.SP.5) Report the number of observations. (6.SP.5) Describe the nature of the attribute under investigation. (6.SP.5)
Give quantitative measures of center and variability as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (6.SP.5) Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (6.SP.5)
Class Title: 6 th Grade Math Grade Level: Math Nine Weeks: 4 th Nine Weeks Unit 8 CCSS: Formula and Graphs Skills: Students will be able to Define independent and dependent variables. (6.EE.9) Use variables to represent two quantities in a real-world problem that change in relationship to one another. (6.EE.9) Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. (6.EE.9) Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (6.EE.9) Solve real-world problems by graphing points in all four quadrants of the coordinate plane. (6.NS.8) Represent and analyze quantitative relationships between dependent and independent variables. Apply and extend previous understandings of numbers to the system of rational numbers. Summarize and describe distributions. Solve real-world and mathematical problems involving area, surface area, and volume. Solve real-world and mathematical problems involving area, surface area, and volume. Use coordinates to find distances between points with the same first coordinate or the same second coordinate. (6.NS.8) Use absolute value to find distances between points with the same first coordinate or the same second coordinate. (6.NS.8) Display numerical data in plots on a number line, dot plots, histograms and box plots. (6.SP.4) Calculate the volume of a right rectangular prism. (6.G.2)
Apply the formula to solve real world mathematical problems involving volume with fractional edge lengths. (6.G.2)
Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 1st Unit: CCSS Unit 1: Ratios and Proportionality Compute unit rates involving rational numbers, fractions, and complex fractions. (7.RP.1) Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute ratios of length in like or different units. (7.RP.1) Compute ratios of area and other measurements in like or different units. (7.RP.1) Determine whether two quantities are in a proportional relationship by using a table and or graph. (7.RP.2) Identify the constant of proportionality (unit rate) in tables, graphs, diagrams, and verbal descriptions. (7.RP.2) Create and solve equations to represent proportional relationships. (7.RP.2) Use words to describe the location of a point on a graph and its relationship to the origin. (7.RP.2) Explain what a point on a graph of a proportional relationship means in terms of the situation. (how does the one quantity relate to the other) (7.RP.2)
Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 1st Unit: CCSS Unit 2: Ratio and Proportion Application Solve multi-step ratio and percent problems. (7.RP.3) Solve problems involving simple interest and tax. (7.RP.3) Solve problems involving markups and markdowns, gratuities and commissions, and fees. (7.RP.3) Analyze proportional relationships and use them to solve real-world and mathematical problems. Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving percent increase, percent decrease, and percent (margin of) error. (7.RP.3) Solve problems involving scale drawings of geometric figures. (7.G.1) Compute actual lengths and areas from a scale drawing. (7.G.1) Reproduce a scale drawing at a different scale. (7.G.1)
Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 2 nd Unit: CCSS Unit 3: Rational Number Operations Add and subtract rational numbers. (7.NS.1) Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1) Use words, visuals, and symbols to describe situations in which opposite quantities combine to make 0. (7.NS.1) Represent addition of quantities with symbols, visuals, and words by showing positive or negative direction from one quantity to the other. (7.NS.1) Show that a number and its opposite have a sum of 0 using visuals, symbols, words, and real-world contexts. (7.NS.1) Use the term additive inverse to describe 2 numbers whose sum is zero. (7.NS.1) Use commutative, distributive, associative, identity, and inverse properties to add and subtract rational numbers. (7.NS.1) Use the term absolute value to describe the distance from zero on number line diagram and with symbols. (7.NS.1) Multiply and divide rational numbers. (7.NS.2)
Use the distributive property to multiply positive and negative rational numbers using symbols, visuals, words, and real-life contexts (7.NS.2) Interpret products of rational numbers by describing real-world contexts. (7.NS.2) Identify situations when integers can and cannot be divided. (7.NS.2) Use words and real-world contexts to explain why the quotient of two integers is a rational number. (7.NS.2) Identify and apply properties used when multiplying and dividing rational numbers. (7.NS.2) Convert a rational number to a decimal using long division. (7.NS.2) Identify terminating or repeating decimal representations of rational numbers. (7.NS.2) Solve real-world and mathematical problems involving the four operations with rational numbers. (7.NS.3)
Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 2 nd Unit: CCSS Unit 4: Expressions Use properties of operations to generate equivalent expressions Use Commutative, Associative, Distributive, Identity, and Inverse Properties to add and subtract linear expressions with rational coefficients. (7.EE.1) Use Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients. (7.EE.1) Rewrite an expression in a different form. (7.EE.2) Choose the form of an expression that works best to solve a problem. (7.EE.2) Explain your reasoning for the choice of expression used to solve a problem. (7.EE.2)
Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 3 rd Unit: CCSS Unit 5: Equations Use commutative, associative, distributive, identity, and inverse properties to calculate with numbers in any form (whole numbers, fractions and decimals). (7.EE.3) Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Convert between rational number forms (whole numbers, fractions and decimals) to solve problems as appropriate. (7.EE.3) Solve multi-step mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. (7.EE.3) Solve multi-step real-life problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. (7.EE.3) Use mental computation and estimation strategies to assess the reasonableness of the answer. (7.EE.3) Translate words or real-life situations into variable equations. (7.EE.4) Translate words or real-life situations into variable inequalities. (7.EE.4) Solve one- or two-step equations with rational numbers fluently.
(7.EE.4) Solve word problems leading to one- or two-step equations with rational numbers. (7.EE.4) Construct simple equations and inequalities with rational numbers to solve problems. (7.EE.4) Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (7.EE.4) Solve word problems leading to one- or two-step inequalities with rational numbers. (7.EE.4) Graph the solution set of inequalities and interpret it in the context of the problem. (7.EE.4) Know the formulas for the area and circumference of a circle. (7.G.4) Use the formulas for area and circumference of a circle to solve problems. (7.G.4) Informally, derive the area formula for a circle based on circumference. (7.G.4)
Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 3 rd Unit: CCSS Unit 6: Data Distributions Recognize and identify that different sampling techniques must be used in real life situations, because it is very difficult to survey an entire population. (7.SP.1) Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations Select appropriate sample sizes based on a population in real-life situations and explain why generalizations about a population from a sample are valid only if the sample is random and representative of that population. (7.SP.1) Collect data from a sample population in order to predict information about a population. (7.SP.1) Interpret data from a random sample to draw inferences about a population with an unknown characteristic of interest. (7.SP.2) Generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing the samples. (7.SP.2) Identify the degree of overlap between two numerical sets of data. (7.SP.3) Visually compare two numerical data distributions with like ranges. (7.SP.3)
Measure the difference between the centers of two different data distributions and express this difference as a multiple of a measure of variability. (7.SP.3) Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 4th Unit: CCSS Unit 8: Geometric Measure Use freehand, ruler, protractor and technology to draw geometric shapes with given conditions. (7.G.2) Construct triangles from 3 measures of angles or sides. (7.G.2) Draw, Construct, and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems in involving angle measure, area, surface area, and volume. Given conditions, determine what and how many type(s) of triangles are possible to construct. (7.G.2) Describe the two-dimensional figures that result from slicing threedimensional figures (right rectangular prisms and right rectangular pyramids). (7.G.3) Identify and describe supplementary, complementary, vertical, and adjacent angles. (7.G.5) Use understandings of supplementary, complementary, vertical and
adjacent angles to write and solve equations. (7.G.5) Explain (verbally and in writing) the relationships between the angles formed by two intersecting lines. (7.G.5) Solve mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (7.G.6) Solve real-world problems involving area, volume and surface area of twoand three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms (7.G.6) Class Title: 7 th Grade Math Grade Level: 7th Nine Weeks: 4th Unit: CCSS Unit 7: Probability Represent the probability of a chance event as a number between 0 and 1. (7.SP.5) Investigate chance processes and develop, use and evaluate probability models. Use the terms likely, unlikely, to describe the probability represented by the fractions used. (7.SP.5) Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency. (7.SP.6) Predict the approximate relative frequency of a chance event given the probability. (7.SP.6)
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (7.SP.7) Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. (7.SP.7) Compare probabilities from a model to observed frequencies. (7.SP.7) If the agreement between a model and observed frequencies is not good, explain possible sources of the discrepancy. (7.SP.7) Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (7.SP.8) Represent the probability of a compound event as the fraction of outcomes in the sample space for which the compound event occurs. (7.SP.8) Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. (7.SP.8) For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. (7.SP.8) Design and use a simulation to generate frequencies for compound events. (7.SP.8)
Class Title: 8th Grade Math Grade Level: 8th Nine Weeks: 1st Unit: CCSS Unit 1: Real Numbers and Exponents Distinguish between rational and irrational numbers. (8.NS.1) Convert a decimal expansion which repeats eventually into a rational number. (8.NS.1) Convert a fraction into a repeating decimal. (8.NS.1) Know that there are numbers that are not rational, and approximate them by rational numbers. Work with radicals and integer exponents. Find rational approximations of irrational numbers. (8.NS.2) Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.(8.ns.2) Evaluate square roots of small perfect squares and cube roots of small perfect cubes. (8.EE.2) Use square root and cube root symbols to solve and represent solutions of equations. (8.EE.2) Apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1) Estimate very large or very small quantities using a single digit times a power of ten. (8.EE.3)
Express how much larger one number expressed as a single digit times a power of ten is than another in the context of the situation. (8.EE.3) Express numbers in scientific notation. (8.EE.4) Perform operations with numbers expressed in scientific notation and a mix of scientific notation and decimal notation. (8.EE.4) Choose appropriate units of measurements for a given number in scientific notation. (8.EE.4) Interpret scientific notation that has been generated by technology. (8.EE.4)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 1st Unit: CCSS Unit 2: Expressions and Equations Simplify linear expressions utilizing the distributive property and collecting like terms. (8.EE.7) Analyze and solve linear equations. Create a multi-step linear equation to represent a real-life situation. (8.EE.7) Solve equations with linear expressions on either or both sides including equations with one solution, infinitely many solutions, and no solutions. (8.EE.7) Give examples of and identify equations as having one solution, infinitely many solutions, or no solutions. (8.EE.7)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 2 nd Unit: CCSS Unit 3: Congruence & Similarity Describe a series of transformations that exhibits congruence between two congruent figures. (8.G.2) Understand congruence and similarity using physical models, transparencies, or geometry software. Describe transformations (dilations, translations, rotations, and reflections) with words and with coordinates. Note that dilations can have centers other than (0,0). (8.G.3) Describe a series of transformations that exhibits similarity between two similar figures. (8.G.4) Find the measures of angles using transversals, the sum of angles in a triangle, the exterior angles of triangles. (8.G.5) Determine if triangles are similar using the angle-angle criterion. (8.G.5) Justify congruence or similarity of figures using a series of transformations. (8.G.2 and 8.G.4)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 2 nd Unit: CCSS Unit 4: Functions Verify that a relationship is a function or not. (8.F.1) Reason from a context, graph, or table after knowing which quantity is the input and which is the output. (8.F.1) Understand the connections between proportional relationships, lines, and linear equations. Define, evaluate, and compare functions. Represent and compare functions numerically, graphically, verbally and algebraically. (8.F.2) Interpret equations in form y = mx + b as a linear function. (8.F.3) Determine whether a function is linear or non-linear. (8.F.3) Identify and contextualize the rate of change and the initial value from tables, graphs, equations, or verbal descriptions. (8.F.4) Construct a model for a linear function. (8.F.4) Describe the qualities of a function using a graph (e.g., where the function is increasing or decreasing). (8.F.5) Sketch a graph when given a verbal description of a situation. (8.F.5) Compare graphs, tables, and equations of proportional relationships. (8.EE.5)
Graph proportional relationships and interpret the unit rate as the slope. (8.EE.5) Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. (8.EE.6) Derive the equation y = mx for a line through the origin and y = mx + b for a line intercepting the vertical axis at. (8.EE.6)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 3 rd Unit: CCSS Unit 5: Linear Relationships Estimate solutions by graphing equations. (8.EE.8) Solve systems by graphing, substitution, or elimination (combination). (8.EE.8) Analyze and solve linear equations and pairs of simulations linear equations. Determine if a system has one solution, no solutions, or many solutions. (8.EE.8) Interpret the solution to a system of equations in context. (8.EE.8)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 3 rd Unit: CCSS Unit 6: Pythagorean Theorem Explain a proof of the Pythagorean Theorem and its converse. (8.G.6) Understand and apply the Pythagorean Theorem Use the Pythagorean Theorem to solve for a missing side of a right triangle given the other 2 sides in both 2-D and 3-D problems. (8.G.7) Apply the Pythagorean Theorem to solve problems in real-world contexts. (8.G.7) Apply the Pythagorean Theorem to find the distance between two points in the coordinate system. (8.G.8)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 4th Unit: CCSS Unit 7: Volume Find the volume of rounded objects in real-world contexts. (8.G.9) Give volume in terms of π and using π 3.14 or 22 7. (8.G.9) Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Find a missing dimension given the volume of rounded object. (8.G.9)
Class Title: 8 th Grade Math Grade Level: 8th Nine Weeks: 4th Unit: CCSS Unit 8: Patterns & Bivariate Data Construct and interpret scatter plots and two-way tables for patterns such as positive or negative association, linearity or curvature, and outliers. (8.SP.1) Investigate patterns of associations in bivariate data. Generate an approximate line of best fit. (8.SP.2) Use the equation of a linear model to solve problems in the context of bivariate measurement data. (8.SP.3) Interpret the slope and y-intercept of the line of best fit in context. (8.SP.3) Show that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. (8.SP.4) Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. (8.SP.4) Use relative frequencies calculated for rows or columns to describe possible association between the two variables. (8.SP.4)